Geodesic
Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 505-522 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar{N},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.
In this paper we investigate linear operators between arbitrary BK spaces $X$ and spaces $Y$ of sequences that are $(\bar{N},q)$ summable or bounded. We give necessary and sufficient conditions for infinite matrices $A$ to map $X$ into $Y$. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for $A$ to be a compact operator.
Classification : 40H05, 46A45, 47B07, 47B37
Keywords: BK spaces; bases; matrix transformations; measure of noncompactness 
@article{CMJ_2001_51_3_a5,
     author = {Malkowsky, E. and Rako\v{c}evi\'c, V.},
     title = {Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded},
     journal = {Czechoslovak Mathematical Journal},
     pages = {505--522},
     year = {2001},
     volume = {51},
     number = {3},
     mrnumber = {1851544},
     zbl = {1079.46504},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a5/}
}
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Malkowsky, E.; Rakočević, V. Measure of noncompactness of linear operators between spaces of sequences that are $(\bar{N},q)$ summable or bounded. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 505-522. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a5/